A new study out of the National Bureau of Economics Research examined the careers of eminent inventors and Nobel Prize winning scientists and found that – at least for history's greatest minds – the genius and innovation required for "great scientific output" seem to peak in the late thirties.

Authors Benjamin Jones, E.J. Reedy and Bruce Weinberg examined the relationship between age and scientific genius for a working paper (i.e. not peer reviewed, or vetted by the NBER Board of Directors) prepared for the forthcoming book Handbook of Genius, and to be "circulated for discussion and comment purposes." In other words, the researchers' conclusions, and the above graph, are to be taken with a bit of salt – but their findings are nonetheless thought provoking. As the authors write:

The literature on age and scientific genius has classically emphasized the peak age of
contributions. The expansive work of Lehman (1953), like other major contributions such as
Zuckerman (1977) and Simonton (1991), estimated the age of peak performance in various fields and then emphasized cross-field comparisons, where the age-output profile was considered fixed
within a particular field. A classic finding is that peak performance has come earlier on average
in mathematics and the physical sciences than in fields like medicine. This cross-field variation
can then be used to make distinctions in the nature of creativity across fields and further inform
theories relating age and genius.

The most obvious factor is education: Scientists spend ages 5 through 18 in school, and then ages 18 through 30ish getting their academic degrees. Then a few years of learning on the job, and presto! You dig up an uncertainty principle. Meanwhile, scientific breakthroughs tend to be less common in old age because we invest less in learning as we get older, and our skills gradually become less relevant.

The idea that modern scientists must learn more than their predecessors did before they can hit upon a breakthrough (what Jones calls the "Burden of Knowledge" theory) could also explain why innovators, on average, appeared to be peak later and later in life throughout the 20th Century:

Read the full working paper here. For some musings on age-dependent genius in the sciences relative to the humanities, see Khazan's piece at The Atlantic.